i would like to mention that mp3tags in the file (most files are tagged) may raise this behave.
I do not know much about mp3 encoding, but i would guess that a tag is stored at the beginning of a file.

If now someone renders the file straigt from bit 0, the tag is played and may sound like a short pop or glitch.

Don't think that this is the cause here -- in 2016, every library able to play MP3s should be aware of ID3 tags in MP3 files (which were stored at the end of the file many years ago (ID3v1) for similar reasons (software not aware of meta data tags), but are stored as ID3v2 tags in the file header now for a long time, so even the last and smallest MP3 decoder knows that it will be there). Besides that, the MP3 decoder always has to do some header parsing to know about the encoding details (like bitrate etc.).

BTW: Have you already tested this problem with a variety of different MP3s from different sources, with similar results?

Has anybody out there encountered similar problems with playing MP3s from within R'n'D?

Furtheron i tried different mp3 from different manufacturers (game music from other games),
as well as inserting silence at the beginning of a file without any change.

To test it do the following, unzip 12_axes.mp3 from the zip link i had sent you.
Turn off soundeffects and music, start game. Then switch music on and off several times.
you should hear a "pop". Then try dungeon4.mp3 the same way.
With this file the pop appears only every once in a while.
Funny because both files where created the same way.

I was able to reproduce this problem with both the SDL and SDL2 mixer, without finding the root cause, though. But I think I was able to work around it, by using a very short (100 ms) fade-in at the beginning of playing a music file. All cases where I was able to hear that "plop" sound now sound just clean and fine!

The fix will be available in the next release candidate (RC2), hopefully very soon (in a few days).